How to bend painting frame sections in hollow?
You could use a custom bevel profile.
I started with a cube, inset the front and back face, and bridged the edge loops to create a frame.

Select one edge loop and create a bevel with Ctrl + B.
Once you create a bevel, you can open the panel in the bottom left to modify your last action.  Bump up the number of segments and select Custom profile.  You can model your bevel using the curve provided.